论文标题
在线sindhorn：距样本流的最佳运输距离
Online Sinkhorn: Optimal Transport distances from sample streams
论文作者
论文摘要
现在，最佳传输（OT）距离通常被用作ML任务中的损失功能。但是，在任意（即不一定是离散）概率分布之间计算距离距离仍然是一个空旷的问题。本文介绍了两个此类任意分布之间的熵登记的OT距离的新在线估计器。它使用来自两个分布的样品流来迭代地丰富了运输计划的非参数表示。与经典的sndhorn算法相比，我们的方法在每次迭代中都利用新样本，从而可以一致地估计真正的正则化ot距离。我们对在线sindhorn算法的收敛性提供了理论分析，显示了迭代序列的几乎-O（1/N）渐近样品复杂性。我们验证我们的合成1D至10D数据和实际3D形状数据的方法。
Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a new online estimator of entropy-regularized OT distances between two such arbitrary distributions. It uses streams of samples from both distributions to iteratively enrich a non-parametric representation of the transportation plan. Compared to the classic Sinkhorn algorithm, our method leverages new samples at each iteration, which enables a consistent estimation of the true regularized OT distance. We provide a theoretical analysis of the convergence of the online Sinkhorn algorithm, showing a nearly-O(1/n) asymptotic sample complexity for the iterate sequence. We validate our method on synthetic 1D to 10D data and on real 3D shape data.
